Problem: Which of the following numbers is a factor of 186? ${4,6,8,9,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $186$ by each of our answer choices. $186 \div 4 = 46\text{ R }2$ $186 \div 6 = 31$ $186 \div 8 = 23\text{ R }2$ $186 \div 9 = 20\text{ R }6$ $186 \div 14 = 13\text{ R }4$ The only answer choice that divides into $186$ with no remainder is $6$ $ 31$ $6$ $186$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $186$ $186 = 2\times3\times31 6 = 2\times3$ Therefore the only factor of $186$ out of our choices is $6$. We can say that $186$ is divisible by $6$.